If the normals to the curve `y=x^2` at the points `P,Q and R` pas thrugh the points `(0,3/2)`, then find circle circumsecribing the triangle `PQR`.

Find the equation of normal to the curve, y = .x^3 at the point (2,8).

The common tangents to the circle x^2=y^2=2 and the parabola y^(2)=8x touch the circle at the points P,Q and the parabola at the points R,S. Then, the area (in sq units) of the quadrilateral PQRS is

Find the equation of the normal to the curve y = x^3 at the point (2,1).

Tangents PA and PB are drawn to the circle (x+3)^(2)+(y-4)^(2)=1 from a variable point P on y=sin x. Find the locus of the centre of the circle circumscribing triangle PAB.

Tangents PT and QT to the parabola y^2 = 4x intersect at T and the normal drawn at the point P and Q intersect at the point R(9, 6) on the parabola. Find the coordinates of the point T . Show that the equation to the circle circumscribing the quadrilateral PTQR , is (x-2) (x-9) + (y+3) (y-6) = 0 .

Normal at 3 points P, Q, and R on a rectangular hyperbola intersect at a point on a curve the centroid of triangle PQR

Normals at points P, Q and R of the parabola y^(2)=4ax meet in a point. Find the equation of line on which centroid of the triangle PQR lies.

Normals at points P, Q and R of the parabola y^(2)=4ax meet in a point. Find the equation of line on which centroid of the triangle PQR lies.